CT-duality as a local property of the world-sheet

TL;DR

This paper explores the local geometric properties of string world-sheets in antisymmetric backgrounds, introducing CT-duality as a relation between mean extrinsic curvature and mean torsion, extending surface geometry with torsion considerations.

Contribution

It generalizes surface geometry to include torsion and defines CT-duality, linking mean extrinsic curvature and mean torsion for string world-sheets.

Findings

Defined mean extrinsic curvature for Minkowski spaces.

Introduced the concept of mean torsion and dual mean extrinsic curvature.

Established the CT-duality condition as a field equation.

Abstract

In the present article, we study the local features of the world-sheet in the case when probe bosonic string moves in antisymmetric background field. We generalize the geometry of surfaces embedded in space-time to the case when the torsion is present. We define the mean extrinsic curvature for spaces with Minkowski signature and introduce the concept of mean torsion. Its orthogonal projection defines the dual mean extrinsic curvature. In this language, the field equation is just the equality of mean extrinsic curvature and extrinsic mean torsion, which we call CT-duality. To the world-sheet described by this relation we will refer as CT-dual surface.